I would personally define remix (in this context) as taking something, music, video, and other mediums and putting one’s own spin on it. It is imputing your opinion either to enhance, point out a new perspective or to simply ‘poke fun at.’ the original.
For instance there are some videos were the person making the video has added uplifting music and enhanced the video to show something good that the original author failed to do. At the same rate there are videos to poke fun, like having a George Bush speech, uplifting music, and war images scrolling in the background. A remix is to make a point, to sway a vote, to use the devices of rhetoric to employ a view not scene in the original.
Thus, I believe the point of the remix is to put a spin on something already published. To add an opinion or a view that was not seen in the original. The remixer could be adding something new or bringing in a new perspective. With many things in life it is so easy to get bogged down by just your opinion or just one side of things, remixes allow for sides, for things to be viewed as a whole and not in just a singular way. It may be slightly random but it reminded me of a lyric from a song
“You somehow managed to take a tiny percent of yourself, the smallest fraction, and turn it into your only equation. You wouldn’t point to your pinky and say this is my entire body, just like you wouldn’t look at one branch and declare that this is a tree. But, if you add all of the little puzzle pieces together, it makes up one entire picture. All are you are is just a little torn corner of a photograph, but when you put more perspectives together you finally get to see the whole frame.”